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Properties

Label 784.6.m
Level $784$
Weight $6$
Character orbit 784.m
Rep. character $\chi_{784}(197,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $810$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 784.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(784, [\chi])\).

Total New Old
Modular forms 1136 830 306
Cusp forms 1104 810 294
Eisenstein series 32 20 12

Trace form

\( 810 q + 2 q^{2} + 2 q^{3} + 24 q^{4} + 2 q^{5} + 116 q^{6} - 256 q^{8} + O(q^{10}) \) \( 810 q + 2 q^{2} + 2 q^{3} + 24 q^{4} + 2 q^{5} + 116 q^{6} - 256 q^{8} + 636 q^{10} + 606 q^{11} + 8 q^{12} + 2 q^{13} + 1780 q^{15} + 3312 q^{16} + 4 q^{17} + 3522 q^{18} - 2358 q^{19} - 4624 q^{20} + 1152 q^{22} - 2648 q^{24} + 7372 q^{26} + 3248 q^{27} - 4082 q^{29} + 2128 q^{30} + 11536 q^{31} - 20168 q^{32} + 4 q^{33} + 23000 q^{34} - 28372 q^{36} + 10650 q^{37} + 18432 q^{38} - 44092 q^{40} + 16682 q^{43} + 19432 q^{44} - 5762 q^{45} - 42252 q^{46} - 44176 q^{47} + 35620 q^{48} + 846 q^{50} - 21048 q^{51} + 5116 q^{52} - 24726 q^{53} - 92032 q^{54} - 93780 q^{58} - 770 q^{59} + 105620 q^{60} - 48078 q^{61} + 34628 q^{62} + 178968 q^{64} + 27692 q^{65} + 172656 q^{66} + 75210 q^{67} + 163632 q^{68} + 21836 q^{69} - 83268 q^{72} - 216768 q^{74} + 166258 q^{75} - 129524 q^{76} + 213008 q^{78} - 52856 q^{79} - 177524 q^{80} - 4789526 q^{81} - 344900 q^{82} - 101398 q^{83} - 126160 q^{85} + 581180 q^{86} - 20524 q^{88} + 217264 q^{90} - 301860 q^{92} + 178748 q^{93} - 76276 q^{94} - 327220 q^{95} - 8872 q^{96} + 4 q^{97} - 42762 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(784, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)